As it goes, I think the thing you're calling "the usual trick" is somewhat incomplete. There's a technique - which I personally don't care for - for thickening a vocal where you what you describe, but you
also pitch shift the vocals panned to the side by a few cents, one up, the other down.
This creates (supposedly) enough difference between the two sides to create a sense of width. When the two sides aren't different enough, there's no sense of width. You have mono, effectively. And the precedence effect brought about by the delay means it will skew to one side.